Reproducible Documentation of Analysis Study 1

R Version

R.Version()

$platform
[1] "aarch64-apple-darwin20"

$arch
[1] "aarch64"

$os
[1] "darwin20"

$system
[1] "aarch64, darwin20"

$status
[1] ""

$major
[1] "4"

$minor
[1] "2.2"

$year
[1] "2022"

$month
[1] "10"

$day
[1] "31"

$`svn rev`
[1] "83211"

$language
[1] "R"

$version.string
[1] "R version 4.2.2 (2022-10-31)"

$nickname
[1] "Innocent and Trusting"

Import of the Data

The data was assessed with the formr survey framework (Arslan, Walther, and Tata 2020). The raw data was imported via the following code. Please note that the results of the Bayesian Analayses may slightly vary due to the estimation approach.

library(tidyverse)
library(ggforce)
library(lme4)
library(BFpack)
library(hrbrthemes)
library(patchwork)
library(brms)
library(viridis)
library(ggdist)
library(tidybayes)
library(here)
library(skimr)
load(here("data/teachers_study1_N40.RData"))

skim(study1)

set.seed(25051982)

Data Wrangling

# wrangle information on the plot type, ES, ...
plot_info <- study1 %>%
    pivot_longer(2:195, names_to = "variables", values_to = "values", 
                 values_transform = as.character) %>%
    dplyr::filter(str_detect(variables, "plot")) %>% 
    # we only need the rows with info on plots
    tidyr::separate(col = values, into = c("type", "axis", "effsize"), 
                    # separate the info into three columns
                    sep = "_", remove = F) %>%
    dplyr::mutate(plot = variables,       # rename variables for later join
                  type = paste(type, axis, sep = "_")) %>%
    dplyr::select(-variables, -axis)

# wrangle answers to items on each page
item_values <- study1 %>%
    dplyr::select(-c(topic:itemo)) %>%
    pivot_longer(2:169, names_to = "variables", values_to = "values", 
                 values_transform = as.character) %>%
    dplyr::mutate(variables = case_when(      # recode variable names that have
        variables == "sensi_6" ~ "sensi_06",  # accidentally been labeled
        variables == "acccl_6" ~ "acccl_06",  # without zero
        variables == "accu3_6" ~ "accu3_06",
        variables == "accov_6" ~ "accov_06",
        variables == "diffi_6" ~ "diffi_06",
        variables == "infor_6" ~ "infor_06",
        variables == "value_6" ~ "value_06",
        TRUE ~ variables 
    )) %>%
    dplyr::mutate(plot = paste0("plotx_", str_sub(variables, -2, -1)), 
                  # create variable for later join
                  variables = str_sub(variables, 1, -4)) %>%    
    # rename variable names to get a data set 
    # with one line per participant per page
    pivot_wider(id_cols = c(session, plot), names_from = "variables", 
                values_from = "values")

# join the two data sets
study1_w <- full_join(plot_info, item_values, 
                               by = c("session", "plot")) %>% 
    # by participant and page (plot)
    dplyr::select(-values) %>%
    dplyr::mutate(rating_cl = as.numeric(acccl), # some var need to be defined as
                  rating_u3 = as.numeric(accu3), # numeric again
                  rating_ov = as.numeric(accov),
                  diffi = as.numeric(diffi),
                  infor = as.numeric(infor),
                  value = as.numeric(value),
                  effsize = as.numeric(effsize),
                  effsize_cl = case_when( 
                  # there is no negative Cliff's Delta, so we have to compute 
                  # two transformations
                      effsize > 0 ~   (((2*pnorm(effsize/2))-1)/pnorm(effsize/2)),
                  # transform the actual effect size Cohen's d to Cliff's Delta
                      effsize < 0 ~ (- (((2*pnorm(abs(effsize)/2))-1)/pnorm(abs(effsize)/2))) 
                  # transform the actual effect size Cohen's d to Cliff's Delta 
                  # and make it negative as in the item
                  ),
                  effsize_u3 = 1-pnorm(effsize), # reverse so that it fits the direction of the U3 item
                  # transform the actual effect size Cohen's d to Cohen's U3
                  effsize_ov = 2 * pnorm(-abs(effsize) / 2), 
                  # transform the actual effect size Cohen's d to overlap
                  # actual difference of rating relative to depicted effectsize 
                  diff_cl = (rating_cl - effsize_cl)/2,
                  # actual difference of rating relative to depicted effectsize
                  diff_u3 = (rating_u3/100) - effsize_u3,
                  # actual difference of rating relative to depicted effectsize 
                  diff_ov = (rating_ov/100) - effsize_ov,
                  diffi_normed = ((diffi - 1)  / 3) - 1, # transform item to -1 to 1
                  infor_normed = ((infor - 1)  / 3) - 1, # transform item to -1 to 1
                  value_normed = ((value - 1)  / 3) - 1) %>%  # transform item to -1 to 1
    group_by(session) %>% 
    mutate(rating_ov_missconcept = median(rating_ov, na.rm = T) < 68.9,
           rating_u3_missconcept = median(rating_u3, na.rm = T) < 21.2) %>% 
    ungroup() %>% 
    mutate(rating_u3_filtered = ifelse(rating_u3_missconcept == T, NA, rating_u3),
           rating_ov_filtered = ifelse(rating_ov_missconcept == T, NA, rating_ov),
           diff_u3_filtered = (rating_u3_filtered/100) - effsize_u3,
           diff_ov_filtered = (rating_ov_filtered/100) - effsize_ov,
           sensi_binary = ifelse(is.na(sensi), # 1 if NOT "equal"
                                        NA,
                                        as.numeric(!grepl("equal", sensi))),
           sensi_ordinal = ordered(factor(substr(sensi, 55, 100)),
                                   levels = c("inferior",
                                              "equal",
                                              "superior")),
           sensi_binary_filtered = case_when(sensi_ordinal == "equal" ~ 0, 
                                             (sensi_ordinal == "inferior" & 
                                                  effsize < 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize > 0) ~ as.numeric(NA),
                                             (sensi_ordinal == "inferior" & # was not there
                                                  effsize > 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize < 0) ~ 1, 
                                             TRUE ~ as.numeric(NA)), # was 1
           sensi_correct = case_when(sensi_ordinal == "equal" ~ "judged equal", 
                                     (sensi_ordinal == "inferior" & 
                                                  effsize < 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize > 0) ~ "wrong direction",
                                             (sensi_ordinal == "inferior" & # was not there
                                                  effsize > 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize < 0) ~ "right direction", 
                                             TRUE ~ NA_character_),
           effsize_abs = abs(effsize))

skim(study1_w)

Data summary

Name	study1_w
Number of rows	960
Number of columns	34
_______________________
Column type frequency:
character	8
factor	1
logical	2
numeric	23
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1.0	64	64	0	40	0
type	0	1.0	13	19	0	4	0
plot	0	1.0	8	8	0	24	0
sensi	480	0.5	59	62	0	3	0
acccl	480	0.5	1	4	0	11	0
accu3	480	0.5	1	3	0	48	0
accov	480	0.5	1	3	0	52	0
sensi_correct	480	0.5	12	15	0	3	0

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
sensi_ordinal	480	0.5	TRUE	3	sup: 177, inf: 159, equ: 144

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
rating_ov_missconcept	0	1	0.22	FAL: 744, TRU: 216
rating_u3_missconcept	0	1	0.55	TRU: 528, FAL: 432

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
effsize	0	1.00	0.00	0.56	-0.80	-0.50	0.00	0.50	0.80	▇▃▁▃▇
diffi	0	1.00	4.05	1.71	1.00	3.00	4.00	5.00	7.00	▇▆▆▆▇
infor	0	1.00	4.11	1.45	1.00	3.00	4.00	5.00	7.00	▅▅▇▇▅
value	0	1.00	4.13	1.49	1.00	3.00	4.00	5.00	7.00	▅▃▆▇▅
rating_cl	480	0.50	0.01	0.38	-1.00	-0.20	0.00	0.20	1.00	▂▆▇▃▁
rating_u3	480	0.50	26.17	22.60	0.00	6.00	18.00	45.00	100.00	▇▃▃▁▁
rating_ov	480	0.50	71.63	28.63	0.00	65.00	80.00	90.00	100.00	▂▁▁▅▇
effsize_cl	0	1.00	0.00	0.34	-0.47	-0.33	0.00	0.33	0.47	▇▃▁▃▇
effsize_u3	0	1.00	0.50	0.21	0.21	0.31	0.50	0.69	0.79	▇▃▁▃▇
effsize_ov	0	1.00	0.80	0.09	0.69	0.69	0.80	0.92	0.92	▇▁▇▁▇
diff_cl	480	0.50	0.01	0.18	-0.54	-0.06	0.00	0.07	0.64	▁▂▇▂▁
diff_u3	480	0.50	-0.24	0.29	-0.79	-0.49	-0.21	-0.03	0.69	▅▆▇▂▁
diff_ov	480	0.50	-0.09	0.29	-0.92	-0.12	0.01	0.10	0.31	▂▁▁▇▅
diffi_normed	0	1.00	0.02	0.57	-1.00	-0.33	0.00	0.33	1.00	▇▆▆▆▇
infor_normed	0	1.00	0.04	0.48	-1.00	-0.33	0.00	0.33	1.00	▅▅▇▇▅
value_normed	0	1.00	0.04	0.50	-1.00	-0.33	0.00	0.33	1.00	▅▃▆▇▅
rating_u3_filtered	744	0.22	43.06	17.90	0.00	30.00	45.00	55.00	80.00	▂▃▇▇▂
rating_ov_filtered	588	0.39	82.60	16.81	0.00	80.00	85.00	90.00	100.00	▁▁▁▅▇
diff_u3_filtered	744	0.22	-0.06	0.22	-0.79	-0.15	-0.03	0.06	0.54	▁▂▇▅▁
diff_ov_filtered	588	0.39	0.02	0.17	-0.92	-0.02	0.05	0.10	0.31	▁▁▁▇▅
sensi_binary	480	0.50	0.70	0.46	0.00	0.00	1.00	1.00	1.00	▃▁▁▁▇
sensi_binary_filtered	507	0.47	0.68	0.47	0.00	0.00	1.00	1.00	1.00	▃▁▁▁▇
effsize_abs	0	1.00	0.50	0.25	0.20	0.20	0.50	0.80	0.80	▇▁▇▁▇

# create a list of u3_misconceptualizers
u3_misconceptualizers <-
    study1_w %>% 
    filter(rating_u3_missconcept == T) %>% 
    pull(session) %>% 
    unique()

# create a list of ov_misconceptualizers
ov_misconceptualizers <-
    study1_w %>% 
    filter(rating_ov_missconcept == T) %>% 
    pull(session) %>% 
    unique()    

### wrangle time stamp data ####################################################
study1_w_timestamp <- 
    read_csv(here("data/teachers_study1_N40_detailed.csv")) %>% 
    # filter participants from study1_w only
    filter(session %in% study1_w$session) %>% 
    # we only need vars sensitivity or accuracy
    dplyr::filter(str_detect(item_name, "sensi|acccl|accu3|accov")) %>%  
    # create var with plot number
    mutate(plot = paste0("plotx_", str_sub(item_name, -2, -1)),
           # recode wrong item labelling
           plot = ifelse(plot == "plotx__6", "plotx_06", plot)) %>% 
    relocate(session, plot) %>% 
    # delete the page number in item name
    mutate(item_name = str_sub(item_name, 1, 5)) %>%  
    pivot_wider(id_cols = c(session, plot), names_from = item_name, 
                values_from = answered_relative) %>% 
    rowwise() %>%
    # what was the time of the first item to be clicked?
    mutate(effic = min(sensi, acccl, accu3, accov, na.rm=T)) %>%
    ungroup() %>% 
    dplyr::select(session, plot, effic, sensi, acccl, accu3, accov) %>% 
    left_join(., study1_w %>% 
                  select(session, plot, type), by=c("session", "plot")) %>% 
    # generate data set so that the six plots from the same type are ordered
    # one after the other (and not 1-24)
    group_by(session, type) %>% 
    arrange(plot) %>% 
    mutate(plotNrWithin = 1:n()) %>%
    ungroup() %>% 
    group_by(plotNrWithin, type) %>% 
    mutate(effic_10righttrunc = ifelse(effic > quantile(effic, .9), NA, effic),
           effic_05righttrunc = ifelse(effic > quantile(effic, .95), NA, effic),
           log_effic_05righttrunc =log(effic_05righttrunc),
           log_effic_10righttrunc = log(effic_10righttrunc),
           plotNrWithin0 = plotNrWithin -1,
           plotNrWithin_factor = as.factor(plotNrWithin)) %>% 
    ungroup()

skim(study1_w_timestamp)

Data summary

Name	study1_w_timestamp
Number of rows	960
Number of columns	15
_______________________
Column type frequency:
character	3
factor	1
numeric	11
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1	64	64	0	40	0
plot	0	1	8	8	0	24	0
type	0	1	13	19	0	4	0

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
plotNrWithin_factor	0	1	FALSE	6	1: 160, 2: 160, 3: 160, 4: 160

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
effic	0	1.00	28817.81	67778.16	2419.00	9065.93	14866.60	26444.00	1342595.60	▇▁▁▁▁
sensi	480	0.50	22664.69	53591.36	2419.00	7670.72	11408.65	20709.33	684967.00	▇▁▁▁▁
acccl	557	0.42	33590.02	83104.51	3547.30	11650.00	18116.60	32103.65	1349401.70	▇▁▁▁▁
accu3	480	0.50	61388.83	88359.00	5599.30	22174.12	39723.25	70041.55	1342595.60	▇▁▁▁▁
accov	480	0.50	69364.58	90056.87	6901.30	26939.18	46882.25	79074.25	1344927.30	▇▁▁▁▁
plotNrWithin	0	1.00	3.50	1.71	1.00	2.00	3.50	5.00	6.00	▇▃▃▃▃
effic_10righttrunc	96	0.90	16914.40	11789.22	2419.00	8734.20	13402.60	21572.35	89854.90	▇▂▁▁▁
effic_05righttrunc	48	0.95	19435.38	17815.29	2419.00	8910.87	14118.35	23782.15	168247.90	▇▁▁▁▁
log_effic_05righttrunc	48	0.95	9.60	0.71	7.79	9.10	9.56	10.08	12.03	▂▇▇▃▁
log_effic_10righttrunc	96	0.90	9.53	0.64	7.79	9.08	9.50	9.98	11.41	▁▆▇▅▁
plotNrWithin0	0	1.00	2.50	1.71	0.00	1.00	2.50	4.00	5.00	▇▃▃▃▃

Sample Description

Sociodemographics

# socio demographics 
sociodemographics <- read_delim("data/teachers_study1a.csv", delim = ";") %>%
    select(session, mcstu, texpe, mcsub) %>% 
    # filter(!is.na(mcstu & texpe)) %>%
    mutate(reply = session %in% c(study1_w$session)) %>%
    filter(!reply == "FALSE") %>%
    select(-reply) %>%
    mutate(mcstu = as.factor(mcstu),
    texpe = as.numeric(texpe),
    mcsub = as.factor(mcsub),
    subject_stem = grepl("1", mcsub),
    subject_languages = grepl("2", mcsub),
    subject_humanities_socialscience = grepl("3", mcsub),
    subject_asthetic = grepl("4", mcsub)) 

skim(sociodemographics) 

Data summary

Name	sociodemographics
Number of rows	40
Number of columns	8
_______________________
Column type frequency:
character	1
factor	2
logical	4
numeric	1
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1	64	64	0	40	0

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
mcstu	0	1	FALSE	6	6: 15, 1: 9, 2: 7, 3: 6
mcsub	0	1	FALSE	10	1: 8, 3: 8, 2: 7, 1, : 3

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
subject_stem	0	1	0.48	FAL: 21, TRU: 19
subject_languages	0	1	0.45	FAL: 22, TRU: 18
subject_humanities_socialscience	0	1	0.50	FAL: 20, TRU: 20
subject_asthetic	0	1	0.15	FAL: 34, TRU: 6

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
texpe	0	1	10.15	8.66	2	4	7	13.5	37.5	▇▃▂▁▁

study1_w_demo <- full_join(study1_w, sociodemographics, by = "session") %>%
    mutate(schooltype_binary = ifelse(mcstu == 6, 1, 0)) # 6 = other

N = 15 participants checked “other” when asked which school type they teach at. This might be problematic as we cannot guarantee that these participants are actual school teachers. Hence, we decided to explore difference between those participants who checked a specific school type and those that checked “other (see section Are there Differences between particpants that indicated a specific school type and those that indicated”other”?).

Descriptives of the Dependent Variables

Descriptives of accuracy and perceived variables across all visualization types

skim(study1_w %>%
         select(diffi,infor,value,rating_u3, rating_ov, rating_cl))

Data summary

Name	%>%(…)
Number of rows	960
Number of columns	6
_______________________
Column type frequency:
numeric	6
________________________
Group variables	None

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
diffi	0	1.0	4.05	1.71	1	3.0	4	5.0	7	▇▆▆▆▇
infor	0	1.0	4.11	1.45	1	3.0	4	5.0	7	▅▅▇▇▅
value	0	1.0	4.13	1.49	1	3.0	4	5.0	7	▅▃▆▇▅
rating_u3	480	0.5	26.17	22.60	0	6.0	18	45.0	100	▇▃▃▁▁
rating_ov	480	0.5	71.63	28.63	0	65.0	80	90.0	100	▂▁▁▅▇
rating_cl	480	0.5	0.01	0.38	-1	-0.2	0	0.2	1	▂▆▇▃▁

Descriptives of accuracy and perceived variables grouped by visualization types

skim(study1_w %>%
         select(diffi, infor,value,rating_u3, rating_ov, rating_cl, session, type, plot) %>%
    gather(var, value, diffi, infor,value,rating_u3, rating_ov, rating_cl)%>%
    mutate(variable = paste(var, type, sep = "_"))%>%
    select(-type, -var)%>%
    group_by(session, plot) %>%
    spread(variable, value) %>%
    ungroup())

Data summary

Name	%>%(…)
Number of rows	960
Number of columns	26
_______________________
Column type frequency:
character	2
numeric	24
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1	64	64	0	40	0
plot	0	1	8	8	0	24	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
diffi_gardneraltman_xaxis	720	0.25	3.59	1.87	1	2.00	3.0	5.00	7.0	▇▅▃▃▅
diffi_halfeye_xaxis	720	0.25	4.23	1.54	1	3.00	4.0	6.00	7.0	▅▇▆▆▇
diffi_halfeye_yaxis	720	0.25	4.55	1.58	1	3.00	5.0	6.00	7.0	▃▃▃▆▇
diffi_raincloud_yaxis	720	0.25	3.83	1.68	1	2.75	4.0	5.00	7.0	▇▆▆▅▆
infor_gardneraltman_xaxis	720	0.25	3.80	1.57	1	3.00	4.0	5.00	7.0	▆▅▆▇▃
infor_halfeye_xaxis	720	0.25	4.19	1.34	1	3.00	4.0	5.00	7.0	▃▆▇▇▅
infor_halfeye_yaxis	720	0.25	4.40	1.35	1	3.00	4.5	5.00	7.0	▂▅▇▇▆
infor_raincloud_yaxis	720	0.25	4.04	1.48	1	3.00	4.0	5.00	7.0	▅▃▇▆▅
rating_cl_gardneraltman_xaxis	843	0.12	0.03	0.40	-1	-0.20	0.0	0.20	1.0	▂▅▇▃▁
rating_cl_halfeye_xaxis	834	0.13	0.00	0.36	-1	-0.20	0.0	0.20	1.0	▁▇▇▂▁
rating_cl_halfeye_yaxis	842	0.12	0.01	0.40	-1	-0.20	0.0	0.20	1.0	▂▇▇▃▁
rating_cl_raincloud_yaxis	841	0.12	0.03	0.38	-1	-0.20	0.0	0.20	0.8	▁▃▇▆▂
rating_ov_gardneraltman_xaxis	843	0.12	68.63	30.39	0	60.00	80.0	90.00	100.0	▂▁▂▅▇
rating_ov_halfeye_xaxis	834	0.13	74.73	26.46	0	70.00	85.0	90.00	100.0	▂▁▁▃▇
rating_ov_halfeye_yaxis	842	0.12	70.08	30.92	0	66.25	80.0	90.00	100.0	▂▁▁▅▇
rating_ov_raincloud_yaxis	841	0.12	72.83	26.57	0	67.50	80.0	90.00	100.0	▂▁▁▅▇
rating_u3_gardneraltman_xaxis	843	0.12	26.56	21.61	0	7.00	22.0	45.00	100.0	▇▃▅▁▁
rating_u3_halfeye_xaxis	834	0.13	26.73	23.01	0	5.25	20.0	48.75	80.0	▇▂▂▃▁
rating_u3_halfeye_yaxis	842	0.12	27.08	23.33	0	7.00	15.0	50.00	75.0	▇▁▂▃▁
rating_u3_raincloud_yaxis	841	0.12	24.28	22.54	0	5.50	15.0	40.00	100.0	▇▃▂▁▁
value_gardneraltman_xaxis	720	0.25	3.80	1.51	1	3.00	4.0	5.00	7.0	▆▅▇▇▃
value_halfeye_xaxis	720	0.25	4.31	1.40	1	3.75	5.0	5.00	7.0	▃▃▆▇▅
value_halfeye_yaxis	720	0.25	4.38	1.39	1	4.00	5.0	5.00	7.0	▂▂▅▇▃
value_raincloud_yaxis	720	0.25	4.03	1.58	1	3.00	4.0	5.00	7.0	▆▃▆▇▅

Descriptives of efficiency across visualization types

skim(study1_w_timestamp %>%
    select(effic, session))

Data summary

Name	study1_w_timestamp %>% se…
Number of rows	960
Number of columns	2
_______________________
Column type frequency:
character	1
numeric	1
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1	64	64	0	40	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
effic	0	1	28817.81	67778.16	2419	9065.93	14866.6	26444	1342596	▇▁▁▁▁

Descriptives of efficiency grouped by visualization types

skim(study1_w_timestamp %>%
    select(sensi, effic, session, type, plot) %>%
    gather(var, value, sensi, effic)%>%
    mutate(variable = paste(var, type, sep = "_"))%>%
    select(-type, -var)%>%
    group_by(session, plot) %>%
    spread(variable, value) %>%
    ungroup())

Data summary

Name	%>%(…)
Number of rows	960
Number of columns	10
_______________________
Column type frequency:
character	2
numeric	8
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
session	0	1	64	64	0	40	0
plot	0	1	8	8	0	24	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
effic_gardneraltman_xaxis	720	0.25	35739.25	99037.01	3547.3	10743.50	17592.75	32584.00	1342595.6	▇▁▁▁▁
effic_halfeye_xaxis	720	0.25	27179.72	62047.66	2897.0	8788.35	13740.70	23012.73	684967.0	▇▁▁▁▁
effic_halfeye_yaxis	720	0.25	23954.41	44387.89	2419.0	8960.30	13016.15	23628.10	466834.3	▇▁▁▁▁
effic_raincloud_yaxis	720	0.25	28397.86	52248.67	2769.0	8910.65	14126.85	25963.05	598871.6	▇▁▁▁▁
sensi_gardneraltman_xaxis	837	0.13	20619.07	20690.87	4326.0	8835.95	14150.30	24945.10	140178.2	▇▁▁▁▁
sensi_halfeye_xaxis	846	0.12	23312.30	67326.04	2897.0	7717.35	11111.55	17859.72	684967.0	▇▁▁▁▁
sensi_halfeye_yaxis	838	0.13	21960.91	56691.29	2419.0	6957.90	9894.00	17751.38	466834.3	▇▁▁▁▁
sensi_raincloud_yaxis	839	0.13	24843.57	59244.50	2769.0	6906.80	11178.70	21190.10	598871.6	▇▁▁▁▁

Are there Differences between particpants that indicated a specific school type and those that indicated “other”?

Graphical Overview

study1_w_demo %>% 
    ggplot(., aes(effsize, rating_cl, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth() +
    ylab("Abstract metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

study1_w_demo%>% 
    ggplot(., aes(effsize, rating_u3, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth() +
    ylab("Cohen's U3 metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

study1_w_demo %>% 
    ggplot(., aes(abs(effsize), rating_ov, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth(method = "lm") +
    ylab("Overlap metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

study1_w_demo %>% 
ggplot(., aes(as.factor(schooltype_binary), infor)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Informativity") +
    xlab("School Type 1") +
    theme_modern_rc()

study1_w_demo %>%
ggplot(., aes(as.factor(schooltype_binary), diffi)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Difficulty") +
    xlab("School Type") +
    theme_modern_rc()

study1_w_demo %>%
ggplot(., aes(as.factor(schooltype_binary), value)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Value") +
    xlab("School Type 1=others") +
    theme_modern_rc()

Compute Kendall’s \(\tau\) for rating_cl, rating_u3 and rating_ov

Show the code

## accuracy U3 
### overall 
study1_w_demo %>% 
    do(tau_u3 = unlist(cor(.$effsize, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)

# A tibble: 1 × 1
   tau_u3
    <dbl>
1 -0.0837

Show the code

### grouped by plot type 
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_u3 = unlist(cor(.$effsize, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)

# A tibble: 4 × 2
  type                 tau_u3
  <chr>                 <dbl>
1 gardneraltman_xaxis -0.0334
2 halfeye_xaxis       -0.143 
3 halfeye_yaxis       -0.0423
4 raincloud_yaxis     -0.118 

Show the code

### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_u3a = unlist(cor(.$effsize, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3a)

# A tibble: 2 × 2
  schooltype_binary tau_u3a
              <dbl>   <dbl>
1                 0 -0.0649
2                 1 -0.122 

Show the code

### grouped by school type and plot type
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_u3 = unlist(cor(abs(.$effsize), .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)

# A tibble: 8 × 3
  schooltype_binary type                tau_u3
              <dbl> <chr>                <dbl>
1                 0 gardneraltman_xaxis 0.105 
2                 0 halfeye_xaxis       0.188 
3                 0 halfeye_yaxis       0.210 
4                 0 raincloud_yaxis     0.0956
5                 1 gardneraltman_xaxis 0.0805
6                 1 halfeye_xaxis       0.131 
7                 1 halfeye_yaxis       0.0252
8                 1 raincloud_yaxis     0.133 

Show the code

## overlap 

### overall 
study1_w_demo %>% 
    do(tau_ov = unlist(cor(abs(.$effsize), .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)

# A tibble: 1 × 1
  tau_ov
   <dbl>
1 -0.276

Show the code

### grouped by plot type 
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_ov = unlist(cor(abs(.$effsize), .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)

# A tibble: 4 × 2
  type                tau_ov
  <chr>                <dbl>
1 gardneraltman_xaxis -0.188
2 halfeye_xaxis       -0.228
3 halfeye_yaxis       -0.326
4 raincloud_yaxis     -0.348

Show the code

### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_ov = unlist(cor(abs(.$effsize), .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)

# A tibble: 2 × 2
  schooltype_binary tau_ov
              <dbl>  <dbl>
1                 0 -0.233
2                 1 -0.345

Show the code

### grouped by school type and plot type 
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_ov = unlist(cor(abs(.$effsize), .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)

# A tibble: 8 × 3
  schooltype_binary type                tau_ov
              <dbl> <chr>                <dbl>
1                 0 gardneraltman_xaxis -0.201
2                 0 halfeye_xaxis       -0.105
3                 0 halfeye_yaxis       -0.195
4                 0 raincloud_yaxis     -0.410
5                 1 gardneraltman_xaxis -0.155
6                 1 halfeye_xaxis       -0.434
7                 1 halfeye_yaxis       -0.541
8                 1 raincloud_yaxis     -0.248

Show the code

## Abstract Metric

### overall
study1_w_demo %>% 
    do(tau_cl = unlist(cor(.$effsize, .$rating_cl, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_cl)

# A tibble: 1 × 1
  tau_cl
   <dbl>
1  0.449

Show the code

### grouped by plot type
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_cl = unlist(cor(.$effsize, .$rating_cl, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_cl)

# A tibble: 4 × 2
  type                tau_cl
  <chr>                <dbl>
1 gardneraltman_xaxis  0.373
2 halfeye_xaxis        0.548
3 halfeye_yaxis        0.484
4 raincloud_yaxis      0.415

Show the code

### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_cl = unlist(cor(.$effsize, .$rating_cl, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_cl)

# A tibble: 2 × 2
  schooltype_binary tau_cl
              <dbl>  <dbl>
1                 0  0.373
2                 1  0.592

Show the code

### grouped by school type and plot type
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_cl = unlist(cor(.$effsize, .$rating_cl, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_cl)

# A tibble: 8 × 3
  schooltype_binary type                tau_cl
              <dbl> <chr>                <dbl>
1                 0 gardneraltman_xaxis  0.379
2                 0 halfeye_xaxis        0.442
3                 0 halfeye_yaxis        0.421
4                 0 raincloud_yaxis      0.280
5                 1 gardneraltman_xaxis  0.371
6                 1 halfeye_xaxis        0.699
7                 1 halfeye_yaxis        0.590
8                 1 raincloud_yaxis      0.701

Show the code

study1_w_demo_vda <- study1_w_demo %>%
    select(session, plot, rating_ov, rating_cl, rating_u3, schooltype_binary) %>%
    pivot_longer(rating_ov:rating_u3, names_to = "variables", 
                 values_to = "values") %>%
    mutate(var = paste(variables, schooltype_binary, sep = "_")) %>%
    select(-variables, values) %>%
    group_by(session, plot) %>%
    pivot_wider(names_from = "var", values_from = "values")

The results do not substantially differ between the two groups. Hence, we will include the participants indicated “other” school types in the following analyses.

Accuracy

Distribution of the Accuracy Variables

study1_w %>% 
    select(rating_cl, rating_u3, rating_ov) %>% 
    pivot_longer(
        c(rating_cl, rating_u3, rating_ov),
        names_to = "dependent_variable", 
        values_to = "rated_effectsize"
        ) %>% 
    ggplot(., aes(rated_effectsize)) +
    geom_histogram() +
    xlab("Rated effect size") +
    facet_wrap(~dependent_variable, scales = "free_x", 
                labeller = as_labeller(c("rating_cl" = "Abstract metric",
                                         "rating_ov" = "Overlap metric",
                                         "rating_u3" = "Cohen's U3 metric"))) +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"))

Somewhat disturbing is the first mode in rating_ov. Maybe some users confused overlap and non-overlap? Another artifact seems to be the first mode in rating_u3.

Are there Constant Misconceptions per Persons?

ggplot(study1_w %>% 
    select(rating_cl, rating_u3, rating_ov, effsize, effsize_cl, session) %>% 
    pivot_longer(
        c(rating_cl, rating_u3, rating_ov),
        names_to = "operationalization", 
        values_to = "judged_effectsize"
        ),
    aes(judged_effectsize, as.numeric(as.factor(session)),
        color = session)
        ) +
    geom_jitter(height = 0) +
    xlab("Rated effect size") +
    ylab("Participant ID") +
    facet_wrap(~ operationalization, scales = "free_x", 
                labeller = as_labeller(c("rating_cl" = "Abstract metric",
                                         "rating_ov" = "Overlap metric",
                                         "rating_u3" = "Cohen's U3 metric"))) +
    theme_modern_rc() +
    theme(legend.position = "none",
          strip.text = element_text(color = "white"))

Association of Ratings and Actual Effect Size

study1_w %>% 
    ggplot(., aes(effsize, rating_cl)) +
    geom_jitter() +
    stat_smooth() +
    ylab("Abstract metric") +
    xlab("Plotted effect size") +
    theme_modern_rc()

study1_w %>% 
    ggplot(., aes(effsize, rating_u3, color = rating_u3_missconcept)) +
    geom_jitter() +
    stat_smooth() +
    ylab("Cohen's U3 metric") +
    xlab("Plotted effect size") +
    labs(color = "Misconcept") +
    theme_modern_rc()

study1_w %>% 
    ggplot(., aes(abs(effsize), rating_ov, color = rating_ov_missconcept)) +
    geom_jitter() +
    stat_smooth(method = "lm") +
    ylab("Overlap metric") +
    xlab("Plotted effect size") +
    labs(color = "Misconcept") +
    theme_modern_rc()

The correlations underpin the interpretation of the misconceptions. Therefore, we will look at the intercorrelations of the dependent variables.

Compute Kendall’s \(\tau\) for rating_cl, rating_u3 and rating_ov

study1_w %>% 
    group_by(type) %>% 
    do(tau_cl = unlist(cor(.$effsize, .$rating_cl, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_cl)

# A tibble: 4 × 2
  type                tau_cl
  <chr>                <dbl>
1 gardneraltman_xaxis  0.373
2 halfeye_xaxis        0.548
3 halfeye_yaxis        0.484
4 raincloud_yaxis      0.415

study1_w %>% 
    group_by(rating_ov_missconcept, type) %>% 
    do(tau_ov = unlist(cor(abs(.$effsize), .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)

# A tibble: 8 × 3
  rating_ov_missconcept type                 tau_ov
  <lgl>                 <chr>                 <dbl>
1 FALSE                 gardneraltman_xaxis -0.355 
2 FALSE                 halfeye_xaxis       -0.384 
3 FALSE                 halfeye_yaxis       -0.478 
4 FALSE                 raincloud_yaxis     -0.523 
5 TRUE                  gardneraltman_xaxis  0.0236
6 TRUE                  halfeye_xaxis        0.119 
7 TRUE                  halfeye_yaxis        0.0205
8 TRUE                  raincloud_yaxis     -0.220 

study1_w %>% 
    group_by(rating_u3_missconcept, type) %>% 
    do(tau_u3 = cor(.$effsize, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete")) %>% 
    unnest(tau_u3)

# A tibble: 8 × 3
  rating_u3_missconcept type                 tau_u3
  <lgl>                 <chr>                 <dbl>
1 FALSE                 gardneraltman_xaxis -0.298 
2 FALSE                 halfeye_xaxis       -0.471 
3 FALSE                 halfeye_yaxis       -0.263 
4 FALSE                 raincloud_yaxis     -0.321 
5 TRUE                  gardneraltman_xaxis  0.119 
6 TRUE                  halfeye_xaxis       -0.153 
7 TRUE                  halfeye_yaxis       -0.108 
8 TRUE                  raincloud_yaxis     -0.0971

Associations of the Dependent Variables

ggplot(study1_w, 
       aes(rating_cl, rating_u3)) +
    geom_jitter() +
    xlab("Abstract metric") +
    ylab("Cohen's U3 metric") +
    theme_modern_rc() +
ggplot(study1_w, 
       aes(rating_cl, rating_ov)) +
    geom_jitter() +
    xlab("Abstract metric") +
    ylab("Overlap metric") +
    theme_modern_rc() +
ggplot(study1_w, 
       aes(rating_ov, rating_u3)) +
    geom_jitter() +
    xlab("Overlap metric") +
    ylab("Cohen's U3 metric") +
    theme_modern_rc()

Global Under- or Overestimation

study1_w %>% 
    select(diff_cl, diff_u3_filtered, diff_ov_filtered, session, type) %>% 
    gather(dependent_variable, difference_to_true_effsize, 
           diff_cl, diff_u3_filtered, diff_ov_filtered) %>% 
    ggplot(., aes(type, difference_to_true_effsize)) +
    geom_boxplot(alpha = .3) +
    facet_wrap(~dependent_variable, scales = "free_y", 
                labeller = as_labeller(c("diff_cl" = "Abstract metric",
                                         "diff_ov_filtered" = "Overlap metric (filtered)",
                                         "diff_u3_filtered" = "Cohen's U3 metric (filtered)"))) +
    geom_jitter(aes(color = type)) +
    ylab("Difference to true effect size") +
    xlab("Accuracy item") +
    labs(color = "Accuracy item") +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"),
          axis.text.x = element_blank())

Research Question 1

Accuracy abstract metric

Random Intercept Models With and Without Visualization Type

#| results: hide
# Rating abstract metric
mod0_rating_cl <- brm(rating_cl ~ + (1|session), 
                          data = study1_w,
                          iter = 20000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4)
mod1_rating_cl <- brm(rating_cl ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 20000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4)
mod2_rating_cl <- brm(rating_cl ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_rating_cl, mod0_rating_cl)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of mod1_rating_cl over mod0_rating_cl: 694826204706870836493993056927744.00000

bayes_factor(mod2_rating_cl, mod1_rating_cl)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4

Estimated Bayes factor in favor of mod2_rating_cl over mod1_rating_cl: 0.00116

Accuracy Cohen’s U3

Random Intercept Models With and Without Visualization Type

#| results: hide
# Rating Cohen's U3
mod0_rating_u3 <- brm(rating_u3 ~ + (1|session), 
                          data = study1_w%>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_rating_u3 <- brm(rating_u3 ~ effsize + (1|session), 
                          data = study1_w%>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_rating_u3 <- brm(rating_u3 ~ type + effsize + (1|session), 
                          data = study1_w %>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_rating_u3, mod0_rating_u3)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of mod1_rating_u3 over mod0_rating_u3: 1045675345.64844

bayes_factor(mod2_rating_u3, mod1_rating_u3)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of mod2_rating_u3 over mod1_rating_u3: 2421.94363

Accuracy overlap

Random Intercept Models With and Without Visualization Type

#| results: hide
# Rating Overlap
mod0_rating_ov <- brm(rating_ov ~ + (1|session), 
                          data = study1_w%>% 
                              filter(rating_ov_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_rating_ov <- brm(rating_ov ~ effsize + (1|session), 
                          data = study1_w%>% 
                              filter(rating_ov_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_rating_ov <- brm(rating_ov ~ type + effsize + (1|session), 
                          data = study1_w %>% 
                              filter(rating_ov_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_rating_ov, mod0_rating_ov)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4

Estimated Bayes factor in favor of mod1_rating_ov over mod0_rating_ov: 4.88773

bayes_factor(mod2_rating_ov, mod1_rating_ov)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of mod2_rating_ov over mod1_rating_ov: 538.87880

Perceived Difficulty

Graphichal Overview

study1_w %>% 
    ggplot(aes(type, diffi)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Difficulty",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

# Perceived Difficulty
mod0_diffi <- brm(diffi ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_diffi <- brm(diffi ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_diffi <- brm(diffi ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_diffi, mod0_diffi)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of mod1_diffi over mod0_diffi: 0.39668

bayes_factor(mod2_diffi, mod1_diffi)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4

Estimated Bayes factor in favor of mod2_diffi over mod1_diffi: 4836329122674284.00000

Perceived Informativity

Graphical Overview

study1_w %>% 
    ggplot(aes(type, infor)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Informativity",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

# Perceived Informativity
mod0_infor <- brm(infor ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_infor <- brm(infor ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_infor <- brm(infor ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_infor, mod0_infor)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of mod1_infor over mod0_infor: 0.25648

bayes_factor(mod2_infor, mod1_infor)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of mod2_infor over mod1_infor: 743067.29182

Perceived Value

Graphical Overview

study1_w %>% 
    ggplot(aes(type, value)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Perceived Value",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

# Perceived Value 
mod0_value <- brm(value ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_value <- brm(value ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_value <- brm(value ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

bayes_factor(mod1_value, mod0_value)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of mod1_value over mod0_value: 0.21854

bayes_factor(mod2_value, mod1_value)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of mod2_value over mod1_value: 84167314.47037

Table all random intercept models

sjPlot::tab_model(
    mod0_rating_cl, mod0_rating_u3, mod0_rating_ov,
    mod0_diffi, mod0_infor, mod0_value,
    mod1_rating_cl, mod1_rating_u3, mod1_rating_ov,
    mod1_diffi, mod1_infor, mod1_value,
    mod2_rating_cl, mod2_rating_u3, mod2_rating_ov,
    mod2_diffi, mod2_infor, mod2_value
    )

	rating_cl		rating_u3		rating_ov		diffi		infor		value		rating_cl		rating_u3		rating_ov		diffi		infor		value		rating_cl		rating_u3		rating_ov		diffi		infor		value
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	0.02	-0.02 – 0.05	43.13	38.53 – 47.78	82.68	80.17 – 85.24	4.06	3.69 – 4.41	4.11	3.82 – 4.41	4.12	3.79 – 4.47	0.01	-0.02 – 0.04	43.33	38.62 – 48.15	82.69	80.16 – 85.22	4.05	3.69 – 4.43	4.10	3.81 – 4.41	4.12	3.77 – 4.47	0.02	-0.05 – 0.08	42.71	36.98 – 48.51	82.33	78.29 – 86.31	3.59	3.20 – 3.98	3.80	3.47 – 4.11	3.80	3.43 – 4.15
effsize													0.37	0.32 – 0.42	-11.79	-15.35 – -8.24	-1.03	-4.04 – 2.02	-0.09	-0.24 – 0.06	-0.06	-0.19 – 0.07	-0.05	-0.17 – 0.07	0.37	0.32 – 0.42	-11.64	-15.22 – -8.10	-1.09	-4.13 – 1.96	-0.09	-0.23 – 0.05	-0.06	-0.19 – 0.07	-0.05	-0.17 – 0.07
typehalfeye_xaxis																									-0.02	-0.10 – 0.06	0.57	-5.07 – 6.12	2.45	-2.21 – 7.08	0.64	0.41 – 0.87	0.39	0.19 – 0.59	0.51	0.32 – 0.70
typehalfeye_yaxis																									0.00	-0.08 – 0.09	4.05	-1.66 – 9.87	-0.99	-5.82 – 3.81	0.97	0.74 – 1.19	0.60	0.40 – 0.81	0.58	0.40 – 0.77
typeraincloud_yaxis																									0.01	-0.08 – 0.09	-1.84	-7.53 – 3.80	-0.14	-4.91 – 4.73	0.24	0.01 – 0.47	0.24	0.04 – 0.45	0.23	0.04 – 0.42
Random Effects
σ2	0.15		259.06		255.16		1.72		1.32		1.17		0.11		213.76		255.11		1.72		1.32		1.17		0.11		213.00		256.12		1.58		1.27		1.11
τ00	0.00 session		75.53 session		29.93 session		1.31 session		0.86 session		1.15 session		0.00 session		82.56 session		29.69 session		1.31 session		0.87 session		1.14 session		0.00 session		79.83 session		28.81 session		1.31 session		0.87 session		1.15 session
ICC	0.01		0.23		0.10		0.43		0.40		0.50		0.02		0.28		0.10		0.43		0.40		0.49		0.02		0.27		0.10		0.45		0.41		0.51
N	40 session		18 session		31 session		40 session		40 session		40 session		40 session		18 session		31 session		40 session		40 session		40 session		40 session		18 session		31 session		40 session		40 session		40 session
Observations	480		216		372		960		960		960		480		216		372		960		960		960		480		216		372		960		960		960
Marginal R2 / Conditional R2	0.000 / 0.006		0.000 / 0.198		0.000 / 0.098		0.000 / 0.413		0.000 / 0.376		0.000 / 0.475		0.278 / 0.291		0.134 / 0.343		0.002 / 0.101		0.001 / 0.414		0.001 / 0.377		0.000 / 0.476		0.281 / 0.294		0.155 / 0.358		0.015 / 0.111		0.049 / 0.463		0.025 / 0.401		0.026 / 0.501

Sensitivity

Graphical Overview

ggplot(study1_w %>% 
           select(sensi_ordinal, type) %>% 
           na.omit(), aes(sensi_ordinal, 
                          color = sensi_ordinal,
                          fill = sensi_ordinal)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    ggtitle("Sensitivity", "all participants")

ggplot(study1_w %>% 
           select(sensi_ordinal, type, session) %>% 
           na.omit() %>% 
           filter(!session %in% ov_misconceptualizers & 
                      !session %in% u3_misconceptualizers), aes(sensi_ordinal, 
                          color = sensi_ordinal,
                          fill = sensi_ordinal)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    ggtitle("Sensitivity", "without missconceptualizers")

ggplot(study1_w %>% 
           select(sensi_correct, type, session) %>%
           dplyr::filter(!is.na(sensi_correct)),
       aes(sensi_correct, 
           color = sensi_correct,
           fill = sensi_correct)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"),
          axis.text.x = element_text(angle = 45, hjust = 1)) +
    labs(color = "", fill = "") +
    ggtitle("Binary Sensitivity", "without wrong decisions")

ggplot(study1_w %>% 
           select(sensi_binary_filtered, type, session),
       aes(sensi_binary_filtered, 
           color = as.factor(sensi_binary_filtered),
           fill = as.factor(sensi_binary_filtered))) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    labs(color = "", fill = "") +
    ggtitle("Binary Sensitivity", "without wrong decisions (0=equal, 1=right direction)")

Logistic Regressions With and Without Visualization Type

Fitting a series of logistic regressions with non-informative priors

#| results: hide

logreg_mod0 <- brm(
    sensi_binary_filtered ~ +(1 | session),
    family = bernoulli(link = "logit"),
    data = study1_w,
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4
    
)

logreg_mod1 <-
    brm(
        sensi_binary_filtered ~ effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = study1_w,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
        
    )

logreg_mod2 <-
    brm(
        sensi_binary_filtered ~ effsize_abs + type + (1 | session),
        family = bernoulli(link = "logit"),
        data = study1_w,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
        
    )

bayes_factor(logreg_mod1, logreg_mod0)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7

Estimated Bayes factor in favor of logreg_mod1 over logreg_mod0: 431499041030447449032808726528.00000

bayes_factor(logreg_mod2, logreg_mod1)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of logreg_mod2 over logreg_mod1: 16.29452

sjPlot::tab_model(logreg_mod0, logreg_mod1, logreg_mod2, show.icc = TRUE)

	sensi_binary_filtered		sensi_binary_filtered		sensi_binary_filtered
Predictors	Odds Ratios	CI (95%)	Odds Ratios	CI (95%)	Odds Ratios	CI (95%)
Intercept	3.05	1.65 – 6.43	0.11	0.03 – 0.38	0.09	0.02 – 0.33
effsize_abs			2731.40	468.39 – 20448.43	3298.10	537.14 – 24253.62
typehalfeye_xaxis					1.90	0.73 – 4.86
typehalfeye_yaxis					1.80	0.73 – 4.62
typeraincloud_yaxis					0.76	0.31 – 1.90
Random Effects
σ2	3.29		3.29		3.29
τ00	3.87 session		10.09 session		10.92 session
ICC	0.54		0.75		0.77
N	40 session		40 session		40 session
Observations	453		453		453
Marginal R2 / Conditional R2	0.000 / 0.318		0.298 / 0.597		0.304 / 0.603

pp_check(logreg_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Efficiency

Visualisation

Raw data

ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,100000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

5% Percent Truncated

ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic_05righttrunc)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,85000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="5% Truncated Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

10% Percent Truncated

ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic_10righttrunc)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,85000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="10% Truncated Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

log() Transformed

ggplot(study1_w_timestamp, 
       aes(as.factor(plotNrWithin), 
           log(effic_05righttrunc))) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="log Transformed Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

Modeling with {brms}

Efficiency for First Plot

#| error: false
#| warning: false
#| results: hide

study1_w_timestamp_effsize <- study1_w_timestamp %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

plot01_mod0 <-
    brm(log_effic_05righttrunc ~ 1 + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod0) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

#| error: false
#| warning: false
#| results: hide
plot01_mod1 <-
    brm(log_effic_05righttrunc~ 1 + effsize + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod1) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

#| error: false
#| warning: false
#| results: hide
plot01_mod2 <-
    brm(log_effic_05righttrunc ~ 1 + effsize + type + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

#| error: false
#| warning: false
#| results: hide
sjPlot::tab_model(plot01_mod0, plot01_mod1, plot01_mod2)

	log_effic_05righttrunc		log_effic_05righttrunc		log_effic_05righttrunc
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	10.12	9.96 – 10.29	10.13	9.99 – 10.30	10.50	10.35 – 10.67
effsize			-0.00	-0.03 – 0.03	0.00	-0.03 – 0.03
typehalfeye_xaxis					-0.43	-0.47 – -0.39
typehalfeye_yaxis					-0.54	-0.58 – -0.49
typeraincloud_yaxis					-0.50	-0.54 – -0.46
Random Effects
σ2	0.25		0.25		0.20
τ00	0.24 session		0.24 session		0.25 session
ICC	0.49		0.49		0.55
N	40 session		40 session		40 session
Observations	3648		3648		3648
Marginal R2 / Conditional R2	0.000 / 0.458		0.000 / 0.458		0.100 / 0.558

bayes_factor(plot01_mod1, plot01_mod0)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4

Estimated Bayes factor in favor of plot01_mod1 over plot01_mod0: 0.03952

bayes_factor(plot01_mod2, plot01_mod1)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of plot01_mod2 over plot01_mod1: 1737177384906463885335523293251307688580332250974846117681183826468337318220449894034152002909190982252383545864094628988450710393013366287013734138140164096.00000

Efficiency for Last Three Plots

#| error: false
#| warning: false
#| results: hide
plot0306_mod0 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot0306_mod0) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

#| error: false
#| warning: false
#| results: hide
plot0306_mod1 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + effsize +
            (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4)

pp_check(plot0306_mod1) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

#| error: false
#| warning: false
#| results: hide
plot0306_mod2 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + effsize +
            type + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4)

pp_check(plot0306_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

sjPlot::tab_model(plot0306_mod0, plot0306_mod1, plot0306_mod2)

	log_effic_05righttrunc		log_effic_05righttrunc		log_effic_05righttrunc
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	9.47	9.34 – 9.60	9.48	9.35 – 9.60	9.58	9.45 – 9.71
plotNrWithin_factor: plotNrWithin_factor5	-0.01	-0.03 – 0.02	-0.01	-0.03 – 0.02	-0.01	-0.03 – 0.02
plotNrWithin_factor: plotNrWithin_factor6	-0.19	-0.21 – -0.17	-0.19	-0.21 – -0.17	-0.19	-0.22 – -0.17
effsize			0.00	-0.02 – 0.02	0.00	-0.02 – 0.02
typehalfeye_xaxis					-0.13	-0.16 – -0.11
typehalfeye_yaxis					-0.21	-0.23 – -0.18
typeraincloud_yaxis					-0.06	-0.09 – -0.04
Random Effects
σ2	0.24		0.24		0.24
τ00	0.17 session		0.17 session		0.17 session
ICC	0.41		0.42		0.42
N	40 session		40 session		40 session
Observations	10944		10944		10944
Marginal R2 / Conditional R2	0.019 / 0.406		0.019 / 0.406		0.034 / 0.421

bayes_factor(plot0306_mod1, plot0306_mod0)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5

Estimated Bayes factor in favor of plot0306_mod1 over plot0306_mod0: 0.02101

bayes_factor(plot0306_mod2, plot0306_mod1)

Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6

Estimated Bayes factor in favor of plot0306_mod2 over plot0306_mod1: 21778843531985354268731897188593076213024111753416409088.00000

Research Question 2

Contrast Effects

Graphical Overview

#| results: hide

# preparing multilevel model with brms for graphical overview

# rating u3  
mod_plot_ratingu3 <- brm(
    scale(rating_u3) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
) 

plot_ratingu3 <- mod_plot_ratingu3 %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
    stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_text(hjust = 0)) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle("Accuracy in Cohen's U3 Metric")

#| results: hide
# rating ov
mod_plot_ratingov <- brm (
    scale(rating_ov) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_ratingov <- mod_plot_ratingov %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
    stat_halfeye() + 
    theme_ipsum_rc()+
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank(), 
          axis.title.y = element_blank()) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle('Accuracy in Overlap Metric')

#| results: hide
# difficulty
mod_plot_diffi <- brm (
    scale(diffi) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_diffi <- mod_plot_diffi %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
    stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank(), 
          axis.title.y = element_blank()) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle('Perceived Task Difficulty')

#| results: hide
# informativity
mod_plot_infor <- brm (
    scale(infor) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_infor <- mod_plot_infor %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_text(hjust = 0)) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle('Perceived Informativity')

#| results: hide
# value 

mod_plot_value <- brm (
    scale(value) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_value <- mod_plot_value %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank(), 
          axis.title.y = element_blank()) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle('Perceived Value')

# efficiency for the first plot

mod_plot_efficiency1 <-
    brm(
        scale(effic) ~ (1 | type),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        control = list(adapt_delta = .999),
        cores = 4
        
    )
 

plot_efficiency1 <- mod_plot_efficiency1 %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
 # median_qi(type_mean = b_Intercept + r_type, .width = c(.95, .66)) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean #xmin = .lower, xmax = .upper
             )) +
#  geom_pointinterval() +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank(), 
          axis.title.y = element_blank()) +
    #scale_x_continuous(limits=c(-0.6, 0.6)) +
    ggtitle('Efficiency for the First Plot')

plot_contrasteffects <- plot_ratingu3 + plot_ratingov + plot_diffi + plot_infor + plot_value + plot_efficiency1 + 
    plot_layout(ncol=3)

plot_contrasteffects 

# ggsave("www/plot_contrasteffects.png", 
#        plot_contrasteffects,
#        width = 25*.55,
#        height = 16*.55)

Model Contrast Effects with {brms}

# create dummy variables to compare visualization types for those measures that showed evidence for difference (accuracy U3, accuracy overlap, perceived task difficulty, perceived informativity, perceived value, efficiency)

## Gardner Altman Plot vs. Halfeye xaxis
gardneraltman_vs_halfeye_x <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_x = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_xaxis") %>%
    ungroup()

gardneraltman_vs_halfeye_x_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_x = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_xaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

#| results: hide
mod_accu3_gardneraltman_halfeye_x <- 
    brm(scale(rating_u3) ~ dummy_gardneraltman_halfeye_x + effsize + (1|session), 
                          data = gardneraltman_vs_halfeye_x%>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_accov_gardneraltman_halfeye_x <- 
    brm(scale(rating_ov) ~ dummy_gardneraltman_halfeye_x + effsize + (1|session), 
                          data = gardneraltman_vs_halfeye_x%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

#| results: hide
mod_diffi_gardneraltman_halfeye_x <- 
    brm(scale(diffi) ~ dummy_gardneraltman_halfeye_x + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_infor_gardneraltman_halfeye_x <- 
    brm(scale(infor) ~ dummy_gardneraltman_halfeye_x + effsize
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_value_gardneraltman_halfeye_x <- 
    brm(scale(value) ~ dummy_gardneraltman_halfeye_x + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE))

mod_effic01_gardneraltman_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_x + 
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_x_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_gardneraltman_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_x +
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_x_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

                  
## Gardner Altman Plot vs. Halfeye yaxis
gardneraltman_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_y = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()

gardneraltman_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_y = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()  %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")


mod_accu3_gardneraltman_halfeye_y <- 
    brm(scale(rating_u3) ~ dummy_gardneraltman_halfeye_y + effsize + (1|session), 
                          data = gardneraltman_vs_halfeye_y%>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_accov_gardneraltman_halfeye_y <- 
    brm(scale(rating_ov) ~ dummy_gardneraltman_halfeye_y + effsize + (1|session), 
                          data = gardneraltman_vs_halfeye_y%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_diffi_gardneraltman_halfeye_y <- 
    brm(scale(diffi) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_infor_gardneraltman_halfeye_y <- 
    brm(scale(infor) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_gardneraltman_halfeye_y <- 
    brm(scale(value) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic01_gardneraltman_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_y +
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic0306_gardneraltman_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_y + 
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_y_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

## Raincloud Plot vs. Halfeye x axis
raincloud_vs_halfeye_x <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_x = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "raincloud_yaxis") %>%
    ungroup()

raincloud_vs_halfeye_x_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_x = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "raincloud_yaxis" | type == "halfeye_xaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

mod_accu3_raincloud_halfeye_x <- 
    brm(scale(rating_u3) ~ dummy_raincloud_halfeye_x + effsize + (1|session), 
                          data = raincloud_vs_halfeye_x %>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_accov_raincloud_halfeye_x <- 
    brm(scale(rating_ov) ~ dummy_raincloud_halfeye_x + effsize + (1|session), 
                          data = raincloud_vs_halfeye_x %>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_diffi_raincloud_halfeye_x <- 
    brm(scale(diffi) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_infor_raincloud_halfeye_x <- 
    brm(scale(infor) ~ dummy_raincloud_halfeye_x +
        effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_raincloud_halfeye_x <- 
    brm(scale(value) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic01_raincloud_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session),
    data = raincloud_vs_halfeye_x_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_raincloud_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_x +
            effsize + (1|session),
    data = raincloud_vs_halfeye_x_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

##  Raincloud Plot vs.Halfeye yaxis
raincloud_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_y = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_yaxis" | type == "raincloud_yaxis") %>%
    ungroup()

raincloud_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_y = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "raincloud_yaxis" | type == "halfeye_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

mod_accu3_raincloud_halfeye_y <- 
    brm(scale(rating_u3) ~ dummy_raincloud_halfeye_y + effsize + (1|session), 
                          data = raincloud_vs_halfeye_y %>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_accov_raincloud_halfeye_y <- 
    brm(scale(rating_ov) ~ dummy_raincloud_halfeye_y + effsize + (1|session), 
                          data = raincloud_vs_halfeye_y %>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_diffi_raincloud_halfeye_y <- 
    brm(scale(diffi) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_infor_raincloud_halfeye_y <- 
    brm(scale(infor) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_raincloud_halfeye_y <- 
    brm(scale(value) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic01_raincloud_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_y +
            effsize + (1|session),
    data = raincloud_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_raincloud_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_y +
            effsize + (1|session),
    data = raincloud_vs_halfeye_y_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

sjPlot::tab_model(mod_accu3_gardneraltman_halfeye_x, 
        mod_accov_gardneraltman_halfeye_x, mod_diffi_gardneraltman_halfeye_x, 
        mod_infor_gardneraltman_halfeye_x, mod_value_gardneraltman_halfeye_x,
        mod_effic01_gardneraltman_halfeye_x, mod_effic0306_gardneraltman_halfeye_x,
        mod_accu3_gardneraltman_halfeye_y, mod_accov_gardneraltman_halfeye_y, 
        mod_diffi_gardneraltman_halfeye_y, mod_infor_gardneraltman_halfeye_y, 
        mod_value_gardneraltman_halfeye_y,
        mod_effic01_gardneraltman_halfeye_y, mod_effic0306_gardneraltman_halfeye_y,
        mod_accov_raincloud_halfeye_x, mod_diffi_raincloud_halfeye_x, 
        mod_infor_raincloud_halfeye_x, mod_value_raincloud_halfeye_x,
        mod_effic01_raincloud_halfeye_x, mod_effic0306_raincloud_halfeye_x,
        mod_accu3_raincloud_halfeye_y, mod_accov_raincloud_halfeye_y, 
        mod_diffi_raincloud_halfeye_y, mod_infor_raincloud_halfeye_y, 
        mod_value_raincloud_halfeye_y,
        mod_effic01_raincloud_halfeye_y, mod_effic0306_raincloud_halfeye_y)

	scale(rating_u3)		scale(rating_ov)		scale(diffi)		scale(infor)		scale(value)		scale(log_effic_05righttrunc)		scale(log_effic_05righttrunc)		scale(rating_u3)		scale(rating_ov)		scale(diffi)		scale(infor)		scale(value)		scale(log_effic_05righttrunc)		scale(log_effic_05righttrunc)		scale(rating_ov)		scale(diffi)		scale(infor)		scale(value)		scale(log_effic_05righttrunc)		scale(log_effic_05righttrunc)		scale(rating_u3)		scale(rating_ov)		scale(diffi)		scale(infor)		scale(value)		scale(log_effic_05righttrunc)		scale(log_effic_05righttrunc)
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	-0.01	-0.34 – 0.32	-0.11	-0.35 – 0.13	-0.18	-0.43 – 0.08	-0.13	-0.39 – 0.12	-0.17	-0.43 – 0.09	0.33	0.09 – 0.58	0.10	-0.10 – 0.31	-0.16	-0.50 – 0.19	0.01	-0.26 – 0.27	-0.26	-0.50 – -0.02	-0.21	-0.45 – 0.03	-0.20	-0.45 – 0.05	0.40	0.12 – 0.65	0.17	-0.03 – 0.37	-0.11	-0.34 – 0.10	-0.13	-0.37 – 0.13	-0.05	-0.28 – 0.18	-0.10	-0.35 – 0.15	-0.05	-0.34 – 0.23	0.06	-0.14 – 0.28	-0.16	-0.47 – 0.18	0.03	-0.20 – 0.28	-0.23	-0.46 – 0.01	-0.13	-0.35 – 0.10	-0.11	-0.33 – 0.12	0.05	-0.24 – 0.34	0.14	-0.08 – 0.37
dummy_gardneraltman_halfeye_x	0.04	-0.27 – 0.35	0.18	-0.11 – 0.46	0.37	0.25 – 0.49	0.26	0.14 – 0.39	0.35	0.24 – 0.46	-0.69	-0.75 – -0.64	-0.20	-0.24 – -0.16
effsize	-0.72	-1.00 – -0.45	0.04	-0.22 – 0.30	-0.04	-0.15 – 0.06	-0.02	-0.13 – 0.09	-0.05	-0.16 – 0.05	0.00	-0.05 – 0.05	0.00	-0.04 – 0.04	-0.49	-0.83 – -0.17	-0.07	-0.33 – 0.18	-0.04	-0.15 – 0.07	-0.03	-0.15 – 0.10	-0.02	-0.13 – 0.09	0.00	-0.04 – 0.04	0.00	-0.04 – 0.04	-0.07	-0.34 – 0.18	-0.07	-0.19 – 0.04	-0.06	-0.19 – 0.07	-0.05	-0.16 – 0.07	-0.00	-0.05 – 0.05	-0.00	-0.04 – 0.04	-0.53	-0.82 – -0.23	-0.15	-0.41 – 0.11	-0.07	-0.18 – 0.05	-0.06	-0.18 – 0.07	-0.01	-0.13 – 0.10	-0.00	-0.04 – 0.04	0.00	-0.03 – 0.03
dummy_gardneraltman_halfeye_y															0.29	-0.06 – 0.66	-0.04	-0.32 – 0.25	0.54	0.42 – 0.65	0.40	0.27 – 0.54	0.39	0.27 – 0.52	-0.79	-0.84 – -0.74	-0.32	-0.37 – -0.28
dummy_raincloud_halfeye_x																													0.21	-0.08 – 0.51	0.25	0.12 – 0.38	0.10	-0.04 – 0.24	0.19	0.07 – 0.31	0.15	0.10 – 0.20	-0.12	-0.16 – -0.08
dummy_raincloud_halfeye_y																																									0.35	-0.00 – 0.69	-0.05	-0.34 – 0.24	0.43	0.30 – 0.57	0.25	0.11 – 0.39	0.24	0.10 – 0.37	-0.00	-0.05 – 0.05	-0.23	-0.27 – -0.19
Random Effects
σ2	0.64		0.95		0.43		0.46		0.40		0.35		0.58		0.78		0.83		0.46		0.55		0.47		0.25		0.58		0.98		0.55		0.62		0.50		0.31		0.54		0.79		0.92		0.54		0.60		0.53		0.26		0.51
τ00	0.27 session		0.07 session		0.59 session		0.57 session		0.63 session		0.59 session		0.43 session		0.21 session		0.21 session		0.50 session		0.45 session		0.54 session		0.70 session		0.42 session		0.04 session		0.48 session		0.42 session		0.54 session		0.78 session		0.49 session		0.15 session		0.10 session		0.46 session		0.42 session		0.50 session		0.87 session		0.52 session
ICC	0.29		0.07		0.58		0.55		0.62		0.63		0.43		0.21		0.21		0.52		0.45		0.53		0.74		0.42		0.04		0.47		0.40		0.52		0.71		0.48		0.16		0.10		0.46		0.41		0.48		0.77		0.50
N	18 session		31 session		40 session		40 session		40 session		39 session		40 session		18 session		31 session		40 session		40 session		40 session		40 session		40 session		31 session		40 session		40 session		40 session		39 session		40 session		18 session		31 session		40 session		40 session		40 session		40 session		40 session
Observations	109		185		480		480		480		1824		5472		104		177		480		480		480		1824		5472		195		480		480		480		1824		5472		107		187		480		480		480		1824		5472
Marginal R2 / Conditional R2	0.168 / 0.393		0.014 / 0.080		0.036 / 0.579		0.019 / 0.543		0.032 / 0.608		0.118 / 0.653		0.010 / 0.418		0.106 / 0.268		0.008 / 0.203		0.074 / 0.540		0.042 / 0.451		0.040 / 0.533		0.151 / 0.753		0.027 / 0.419		0.018 / 0.055		0.018 / 0.460		0.005 / 0.384		0.011 / 0.508		0.006 / 0.688		0.004 / 0.461		0.131 / 0.261		0.013 / 0.111		0.050 / 0.468		0.019 / 0.407		0.015 / 0.471		0.000 / 0.744		0.013 / 0.487

## Gardner Altman Plot vs. Raincloud Plot
gardneraltman_vs_raincloud <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_raincloud = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "raincloud_yaxis") %>%
    ungroup()

gardneraltman_vs_raincloud_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_raincloud = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "raincloud_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

mod_accu3_gardneraltman_raincloud <- 
    brm(scale(rating_u3) ~ dummy_gardneraltman_raincloud + effsize + (1|session), 
                          data = gardneraltman_vs_raincloud%>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_accov_gardneraltman_raincloud <- 
    brm(scale(rating_ov) ~ dummy_gardneraltman_raincloud + effsize + (1|session), 
                          data = gardneraltman_vs_raincloud%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_diffi_gardneraltman_raincloud <- 
    brm(scale(diffi) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session), 
                          data = gardneraltman_vs_raincloud,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_infor_gardneraltman_raincloud <- 
    brm(scale(infor) ~ dummy_gardneraltman_raincloud +
            effsize + (1|session), 
        data = gardneraltman_vs_raincloud,
        save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_gardneraltman_raincloud <- 
    brm(scale(value) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session), 
                          data = gardneraltman_vs_raincloud,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic01_gardneraltman_raincloud <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session),
    data = gardneraltman_vs_raincloud_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_gardneraltman_raincloud <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session),
    data = gardneraltman_vs_raincloud_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

## Halfeye xaxis vs. Halfeye yaxis

halfeye_x_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_halfeye_x_halfeye_y = 
               case_when(type == "halfeye_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()

halfeye_x_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_halfeye_x_halfeye_y = 
               case_when(type == "halfeye_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "halfeye_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

mod_accu3_halfeye_x_halfeye_y <- 
    brm(scale(rating_u3) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y %>% 
                              filter(rating_u3_missconcept == F),
                          save_pars = save_pars(all = TRUE),
        
    silent = 2,
    refresh = 0,
    cores = 4)

mod_accov_halfeye_x_halfeye_y <- 
    brm(scale(rating_ov) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
        
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 20000)

mod_diffi_halfeye_x_halfeye_y <- 
    brm(scale(diffi) ~ dummy_halfeye_x_halfeye_y +
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE))

mod_infor_halfeye_x_halfeye_y <- 
    brm(scale(infor) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_halfeye_x_halfeye_y <- 
    brm(scale(value) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic01_halfeye_x_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session),
    data = halfeye_x_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    iter = 10000)

mod_effic0306_halfeye_x_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session),
    data = halfeye_x_vs_halfeye_y_effic%>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

sjPlot::tab_model(mod_accu3_halfeye_x_halfeye_y, mod_accov_halfeye_x_halfeye_y, 
                  mod_diffi_halfeye_x_halfeye_y, mod_infor_halfeye_x_halfeye_y, 
                  mod_value_halfeye_x_halfeye_y,
                  mod_effic01_halfeye_x_halfeye_y)

	scale(rating_u3)		scale(rating_ov)		scale(diffi)		scale(infor)		scale(value)		scale(log_effic_05righttrunc)
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	-0.09	-0.42 – 0.23	0.11	-0.10 – 0.32	-0.10	-0.35 – 0.15	-0.07	-0.31 – 0.16	-0.02	-0.28 – 0.26	0.11	-0.17 – 0.38
dummy_halfeye_x_halfeye_y	0.16	-0.17 – 0.50	-0.23	-0.51 – 0.05	0.20	0.08 – 0.33	0.16	0.04 – 0.28	0.05	-0.06 – 0.16	-0.14	-0.20 – -0.08
effsize	-0.67	-0.98 – -0.36	-0.04	-0.31 – 0.22	-0.01	-0.12 – 0.10	0.04	-0.08 – 0.15	0.05	-0.05 – 0.16	-0.00	-0.05 – 0.05
Random Effects
σ2	0.71		0.98		0.48		0.47		0.41		0.37
τ00	0.25 session		0.03 session		0.55 session		0.57 session		0.65 session		0.72 session
ICC	0.26		0.03		0.53		0.55		0.62		0.66
N	18 session		31 session		40 session		40 session		40 session		39 session
Observations	109		194		480		480		480		1824
Marginal R2 / Conditional R2	0.150 / 0.332		0.018 / 0.052		0.012 / 0.521		0.008 / 0.538		0.002 / 0.598		0.005 / 0.626

sjPlot::tab_model(mod_effic0306_halfeye_x_halfeye_y,
                  mod_accu3_gardneraltman_raincloud, 
                  mod_accov_gardneraltman_raincloud, 
                  mod_diffi_gardneraltman_raincloud)

	scale(log_effic_05righttrunc)		scale(rating_u3)		scale(rating_ov)		scale(diffi)
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	0.08	-0.15 – 0.32	0.12	-0.21 – 0.45	0.02	-0.22 – 0.25	-0.06	-0.29 – 0.17
dummy_halfeye_x_halfeye_y	-0.12	-0.16 – -0.09
effsize	0.00	-0.03 – 0.03	-0.69	-0.98 – -0.40	-0.10	-0.34 – 0.15	-0.09	-0.22 – 0.03
dummy_gardneraltman_raincloud			-0.17	-0.52 – 0.16	-0.01	-0.30 – 0.27	0.14	-0.01 – 0.28
Random Effects
σ2	0.52		0.68		0.89		0.59
τ00	0.52 session		0.24 session		0.14 session		0.45 session
ICC	0.50		0.26		0.14		0.44
N	40 session		18 session		31 session		40 session
Observations	5472		107		178		480
Marginal R2 / Conditional R2	0.004 / 0.482		0.161 / 0.354		0.009 / 0.144		0.009 / 0.421

sjPlot::tab_model(mod_infor_gardneraltman_raincloud, 
                  mod_value_gardneraltman_raincloud,
                  mod_effic01_gardneraltman_raincloud, 
                  mod_effic0306_gardneraltman_raincloud)

	scale(infor)		scale(value)		scale(log_effic_05righttrunc)		scale(log_effic_05righttrunc)
Predictors	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)	Estimates	CI (95%)
Intercept	-0.07	-0.29 – 0.15	-0.08	-0.32 – 0.15	0.41	0.15 – 0.68	0.05	-0.16 – 0.26
dummy_gardneraltman_raincloud	0.16	0.02 – 0.30	0.15	0.02 – 0.28	-0.77	-0.81 – -0.72	-0.10	-0.14 – -0.06
effsize	-0.11	-0.24 – 0.01	-0.11	-0.22 – -0.00	-0.00	-0.04 – 0.04	-0.00	-0.04 – 0.04
Random Effects
σ2	0.60		0.50		0.25		0.57
τ00	0.43 session		0.54 session		0.71 session		0.45 session
ICC	0.42		0.52		0.74		0.44
N	40 session		40 session		39 session		40 session
Observations	480		480		1824		5472
Marginal R2 / Conditional R2	0.011 / 0.406		0.010 / 0.506		0.144 / 0.747		0.003 / 0.426

References

Arslan, Ruben C., Matthias P. Walther, and Cyril S. Tata. 2020. “Formr: A Study Framework Allowing for Automated Feedback Generation and Complex Longitudinal Experience-Sampling Studies Using R.” Behavior Research Methods 52 (1): 376–87. https://doi.org/10.3758/s13428-019-01236-y.